Working Paper: NBER ID: w24914
Authors: Nicolas S. Lambert; Giorgio Martini; Michael Ostrovsky
Abstract: We study general quadratic games with multidimensional actions, stochastic payoff interactions, and rich information structures. We first consider games with arbitrary finite information structures. In such games, we show that there generically exists a unique equilibrium. We then extend the result to games with infinite information structures, under an additional assumption of linearity of certain conditional expectations. In that case, there generically exists a unique linear equilibrium. In both cases, the equilibria can be explicitly characterized in compact closed form. We illustrate our results by studying information aggregation in large asymmetric Cournot markets and the effects of stochastic payoff interactions in beauty contests. Our results apply to general games with linear best responses, and also allow us to characterize the effects of small perturbations in arbitrary Bayesian games with finite information structures and smooth payoffs.
Keywords: Quadratic Games; Bayesian Nash Equilibrium; Stochastic Payoff Interactions
JEL Codes: C62; C72; D43; L13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| arbitrary finite information structures (C69) | unique Bayesian Nash equilibrium (C73) |
| infinite information structures (D83) | unique linear equilibrium (C62) |
| market size (L25) | equilibrium quantity (D50) |
| stochastic payoff interactions (C73) | unique equilibria (C62) |
| structure of interactions (L14) | equilibrium outcomes (D51) |